Embittered by the loss of powers under the voter-approved strong-mayor referendum earlier this year, the Miami-Dade County Commission is exploring measures to regain control over county business. In March, against the wishes of Mayor Carlos Alvarez, the commission approved an ordinance that strips the Miami-Dade police's public-corruption unit of independent authority to investigate elected county officials. Now, commissioners are eyeing other proposals, including a measure that would give the commission authority to award bids on construction projects up to $500,000 and on supply contracts less than $1 million.